Fast-Wave Polarization, Charge Horizons, and the Time Evolution of Force-free Magnetospheres

Abstract

Numerical simulations of force-free, degenerate (ffde) pulsar and black hole magnetospheres are often based on 1-D characteristics. In particular, the plasma wave polarizations that can be propagated along the 1-D characteristics determine the time evolution of the entire system. There are two sets of characteristics, corresponding to the fast and Alfven modes. The fast wave is generally considered to be a transverse light wave, however recently it has been claimed that light-like fast waves can transport a longitudinal electric polarization, E , at the speed of light. The implication is quite profound if true, namely that the wrong information has been propagated along the fast characteristics in all previous simulations of force-free magnetospheres. It is shown in this Letter that the light-like fast waves must be transverse and previous simulations are valid. This result is demonstrated by means of a fundamental physical principle (associated with the fact that particles cannot flow faster than the speed of light), there exists a charge horizon in ffde magnetospheres. It is shown that the Alfven critical surfaces in a ffde magnetosphere are both charge and particle horizons, i.e. one way membranes that do not permit traversal by charges nor particles anti-directed to the bulk flow. Since the propagation of a discontinuous change in E requires a physical surface charge on the wave-face, it is also a one-way membrane for longitudinally polarized waves. Besides justifying previous ffde simulations this result also invalidates previous claims that fast waves can radiate E from the event horizon of a black hole.

General relativistic magnetohydrodynamic simulations of monopole magnetospheres of black holes

“…Figure 3 also shows that the Lorentz factor of the ingoing wind remains very low and, thus, there is no any reason for the breakdown of the FFDE approximation at the event horizon suggested in (Punsly 2004;Macdonald & Thorne 1982).…”

“…The very relevant example can be found in the theory of magnetically dominated pulsar winds where particle inertia becomes an important factor as a result of acceleration by electromagnetic field (Mestel 1999, Section 13.2.3) Other potential examples in the theory of black hole magnetospheres are discussed by Punsly (2001, Sections 8 and 9). Recently, Punsly (2004) argued that FFDE is deficient near the event horizon where "the plasma attains an infinite inertia in a global sense". Macdonald and Thorne (1982) also anticipated a breakdown of the FFDE approximation near the event horizon, though no detailed explanations were given.…”

A new solution to the plasma starved event horizon magnetosphere

“…The very tenuous stray charges have trajectories that are affected by these fields, but the number density is too small to provide a source for a significant perturbation to these fields. Charges can only flow inward across the charge horizon (Komissarov 2004;Punsly 2004). flow division surface producing a vacuum gap as depicted in Fig. 3.…”

“…The very tenuous stray charges have trajectories that are affected by these fields, but the number density is too small to provide a source for a significant perturbation to these fields. Charges can only flow inward across the charge horizon (Komissarov 2004;Punsly 2004) portion of the flux tube contracts toward the black hole by gravity and the outer is slung out by magneto-centrifugal forces. Evaluating Maxwell's equations as the inner portion of the flux tube approaches the event horizon indicates that the large scale poloidal magnetic field in the EHM will approximately be a decaying magnetic dipole (see Figure C.2).…”

Riemann solvers and Alfven waves in black hole magnetospheres

“…All inflows must pass through an IACS, thereby rendering the interior region out of Alfven wave communication with the out-flowing wind. Thus, the IACS is a charge horizon (a one-way membrane) for the global flow since the Alfven wave is the only wave that carries a physical charge [Punsly(2004)]. The IACS causally excises most of the active region of space-time (the ergosphere) that would be the putative element to enforce rapid rotation of the system.…”